What is the derivative of ln(1+4/x) ?

The derivative of ln(1+4/x) is -4/(x(x+4))

What is the first derivative of ln(1+4/x) ?

The first derivative of ln(1+4/x) is -4/(x(x+4))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (ln (1 + \frac{4}{x}))

- \frac{4}{x ( x + 4 )}

Solution steps

\frac{d}{d x} (ln (1 + \frac{4}{x}))

Apply the chain rule:

\frac{1}{1 + \frac{4}{x}} \frac{d}{d x} (1 + \frac{4}{x})

= \frac{1}{1 + \frac{4}{x}} \frac{d}{d x} (1 + \frac{4}{x})

\frac{d}{d x} (1 + \frac{4}{x}) = - \frac{4}{x ^{2}}

= \frac{1}{1 + \frac{4}{x}} (- \frac{4}{x ^{2}})

Simplify

\frac{1}{1 + \frac{4}{x}} (- \frac{4}{x ^{2}}) : - \frac{4}{x ( x + 4 )}

= - \frac{4}{x ( x + 4 )}

What is the derivative of ln(1+4/x) ?
The derivative of ln(1+4/x) is -4/(x(x+4))
What is the first derivative of ln(1+4/x) ?
The first derivative of ln(1+4/x) is -4/(x(x+4))